The volume of the parallelopiped whose edges are represented by -… - Vidyadip

MCQ

The volume of the parallelopiped whose edges are represented by $-12 \hat{i}+\alpha \hat{k}, 3 \hat{j}-\hat{k}$ and $2 \hat{ i }+\hat{ j }-15 \hat{ k }$ is 546 . Then $\alpha=$

A
3
B
2
✓
$-3$
D
$-2$

✓

Answer

Correct option: C.

$-3$

(C) Volume of parallelopiped $=\left|\begin{array}{ccc}-12 & 0 & \alpha \\ 0 & 3 & -1 \\ 2 & 1 & -15\end{array}\right|$
$\begin{array}{l}\Rightarrow 546=-12(-45+1)+\alpha(0-6) \\ \Rightarrow \alpha=-3\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Vectors→Vectors — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\sin \left[3 \sin ^{-1}\left(\frac{1}{5}\right)\right]=$

$\int_0^{\pi / 2} \frac{\sin x}{1+\cos ^2 x} d x$ has the value

There are two value of a which makes the determinant $\triangle=\begin{vmatrix}1&-2&5\\2&\text{a}&-1\\0&4&2\text{a}\end{vmatrix}$ equal to $86.$ The sum of these two values is:

In $\triangle A B C, \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=$

The equation of a line passing through point $(1,2,3)$ and perpendicular to the plane $x+2 y-5 z+9=0$ are

The joint equation of pair of straight lines passing through origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is

Let $\overline{a}=\hat{i}-2 \hat{j}+3 \hat{k}$. If $\bar{b}$ is a vector such that $\overline{ a } \cdot \overline{ b }=|\overline{ b }|^2$ and $|\overline{ a }-\overline{ b }|=\sqrt{7}$, then $|\overline{ b }|=$

If $A=\left[\begin{array}{ll}-1 & 5 \\ -3 & 2\end{array}\right]$, then adj $A=$

The vector equation of the plane which is at distance of $\frac{3}{\sqrt{14}}$ from the origin and the normal from the origin is $2 \hat{i}-3 \hat{j}+\hat{k}$ is

Fifteen coupons are numbered $1$ to $15.$ Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is $9$ is: